A249649 Decimal expansion of integral_{0..1} Li_3(x) dx, where Li_3 is the trilogarithm function.

5, 5, 7, 1, 2, 2, 8, 3, 6, 3, 1, 1, 3, 6, 7, 8, 4, 8, 9, 2, 7, 3, 2, 2, 9, 9, 4, 8, 6, 5, 4, 2, 4, 8, 0, 1, 5, 4, 6, 0, 3, 6, 3, 9, 1, 1, 3, 3, 7, 0, 0, 4, 4, 4, 0, 5, 6, 7, 1, 3, 3, 2, 5, 9, 7, 1, 8, 3, 0, 7, 3, 5, 3, 8, 3, 1, 1, 2, 2, 1, 6, 3, 5, 2, 8, 2, 6, 9, 7, 2, 9, 8, 9, 5, 7, 6, 5, 5, 2, 8, 4, 2

Offset

0,1

Links

Table of n, a(n) for n=0..101.

Eric Weisstein's MathWorld, Trilogarithm

Formula

int_{0..1} Li_3(x) dx = 1 - zeta(2) + zeta(3) = 1 - Pi^2/6 + zeta(3).

Compare with the same integral of the dilogarithm:

int_{0..1} Li_2(x) dx = zeta(2) - 1 = Pi^2/6 - 1 = 0.644934...

Example

0.5571228363113678489273229948654248015460363911337...

Mathematica

RealDigits[1 - Zeta[2] + Zeta[3], 10, 102] // First

Crossrefs

Cf. A002117, A013661.

Sequence in context: A348293 A327242 A173932 * A226571 A274030 A061382

Adjacent sequences: A249646 A249647 A249648 * A249650 A249651 A249652

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Nov 03 2014

Status

approved